:=
What does the "colon-equal symbol" mean, and how is it used?
Answer
According to Wikipedia's article on logic symbols, := is used for definition. The truth of a proposition can be determined through empirical or rational means, but sometimes it is assigned axiomatically:
p = q means there is an equivalence of values
p := q means that p is equivalent to q by definition, assignment, or declaration, such as when a mathematician declares something like 'Let p be assigned q', for example.
It has been my experience that the more traditional way to express definition is the use of '≡', but in computer science, since the colon and equal sign are standard on a QWERTY keyboard, it often gains usage because of its syntactic assignment as an assignment operator to avoid confusion with the operation that checks for equality.
See also: SE Philosophy:What's the difference among the logical relations :=, =, and ≡?
Addendum:
As per comments below, note well that other notations such as '≜' and '≝' have been and continue to be used in literature to differentiate definition and equality. As the user mlk notes below, the orthography of ':=' is such that '=:' can be used to indciate that the definition occurs on the left. That is 'p =: q' specifies that q is the definiendum and p is the definiens.